Pub Date : 2019-01-01DOI: 10.4310/ajm.2019.v23.n6.a2
R. De Leo
{"title":"Proof of a Gromov conjecture on the infinitesimal invertibility of the metric-inducing operators","authors":"R. De Leo","doi":"10.4310/ajm.2019.v23.n6.a2","DOIUrl":"https://doi.org/10.4310/ajm.2019.v23.n6.a2","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.4310/AJM.2019.V23.N3.A4
J. Eschenburg, P. Quast, M. Tanaka
{"title":"Isometries of extrinsic symmetric spaces","authors":"J. Eschenburg, P. Quast, M. Tanaka","doi":"10.4310/AJM.2019.V23.N3.A4","DOIUrl":"https://doi.org/10.4310/AJM.2019.V23.N3.A4","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.4310/ajm.2019.v23.n6.a5
Yuejiao Wang, Yingqiu Li, Quansheng Liu, Zaiming Liu
We consider a supercritical branching process $(Z_n)$ in an independent and identically distributed random environment $xi =(xi_n)$. Let $W$ be the limit of the natural martingale $W_n = Z_n / E_xi Z_n (n geq 0)$, where $E_xi $ denotes the conditional expectation given the environment $xi$. We find a necessary and sufficient condition for the existence of quenched weighted moments of $W$ of the form $E_{xi} W^{alpha} l(W)$, where $alpha > 1$ and $l$ is a positive function slowly varying at $infty$. The same conclusion is also proved for the maximum of the martingale $W^* = sup_{ngeq 1} W_n $ instead of the limit variable $W$. In the proof we first show an extended version of Doob's inequality about weighted moments for nonnegative submartingales, which is of independent interest.
{"title":"Quenched weighted moments of a supercritical branching process in a random environment","authors":"Yuejiao Wang, Yingqiu Li, Quansheng Liu, Zaiming Liu","doi":"10.4310/ajm.2019.v23.n6.a5","DOIUrl":"https://doi.org/10.4310/ajm.2019.v23.n6.a5","url":null,"abstract":"We consider a supercritical branching process $(Z_n)$ in an independent and identically distributed random environment $xi =(xi_n)$. Let $W$ be the limit of the natural martingale $W_n = Z_n / E_xi Z_n (n geq 0)$, where $E_xi $ denotes the conditional expectation given the environment $xi$. We find a necessary and sufficient condition for the existence of quenched weighted moments of $W$ of the form $E_{xi} W^{alpha} l(W)$, where $alpha > 1$ and $l$ is a positive function slowly varying at $infty$. The same conclusion is also proved for the maximum of the martingale $W^* = sup_{ngeq 1} W_n $ instead of the limit variable $W$. In the proof we first show an extended version of Doob's inequality about weighted moments for nonnegative submartingales, which is of independent interest.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.4310/ajm.2019.v23.n1.a1
Gennaro di Brino
{"title":"The $mathit{Quot}$ functor of a quasi-coherent sheaf","authors":"Gennaro di Brino","doi":"10.4310/ajm.2019.v23.n1.a1","DOIUrl":"https://doi.org/10.4310/ajm.2019.v23.n1.a1","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70390840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.4310/ajm.2019.v23.n4.a5
Ji Shi, Xiuqiong Chen, S. Yau
{"title":"High order linear extended state observer and error analysis of active disturbance rejection control","authors":"Ji Shi, Xiuqiong Chen, S. Yau","doi":"10.4310/ajm.2019.v23.n4.a5","DOIUrl":"https://doi.org/10.4310/ajm.2019.v23.n4.a5","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.4310/AJM.2019.V23.N1.A2
D. Gu, F. Luo, Tianqi Wu
The classical uniformization theorem of Poincaré and Koebe states that any simply connected surface with a Riemannian metric is conformally diffeomorphic to the Riemann sphere, or the complex plane or the unit disk. Using the work by Gu-Luo-Sun-Wu [9] on discrete conformal geometry for polyhedral surfaces, we show that the uniformization maps for simply connected Riemann surfaces are computable.
庞加莱和柯比的经典均匀化定理指出，任何具有黎曼度规的单连通曲面都与黎曼球、复平面或单位盘共形微分同态。利用guu - luo - sun - wu[9]在多面体曲面的离散共形几何上的工作，我们证明了单连通黎曼曲面的均匀化映射是可计算的。
{"title":"Convergence of discrete conformal geometry and computation of uniformization maps","authors":"D. Gu, F. Luo, Tianqi Wu","doi":"10.4310/AJM.2019.V23.N1.A2","DOIUrl":"https://doi.org/10.4310/AJM.2019.V23.N1.A2","url":null,"abstract":"The classical uniformization theorem of Poincaré and Koebe states that any simply connected surface with a Riemannian metric is conformally diffeomorphic to the Riemann sphere, or the complex plane or the unit disk. Using the work by Gu-Luo-Sun-Wu [9] on discrete conformal geometry for polyhedral surfaces, we show that the uniformization maps for simply connected Riemann surfaces are computable.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-28DOI: 10.4310/ajm.2021.v25.n2.a7
Rong Du, X. Fang
We study the normal bundles of the exceptional sets of isolated simple small singularities in the higher dimension when the Picard group of the exceptional set is $mathbb{Z}$ and the normal bundle of it has some good filtration. In particular, for the exceptional set is a projective space with the split normal bundle, we generalized Nakayama and Ando's results to higher dimension. Moreover, we also generalize Laufer's results of rationality and embedding dimension to higher dimension.
{"title":"Normal bundles on the exceptional sets of simple small resolutions","authors":"Rong Du, X. Fang","doi":"10.4310/ajm.2021.v25.n2.a7","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n2.a7","url":null,"abstract":"We study the normal bundles of the exceptional sets of isolated simple small singularities in the higher dimension when the Picard group of the exceptional set is $mathbb{Z}$ and the normal bundle of it has some good filtration. In particular, for the exceptional set is a projective space with the split normal bundle, we generalized Nakayama and Ando's results to higher dimension. Moreover, we also generalize Laufer's results of rationality and embedding dimension to higher dimension.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48210628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-06DOI: 10.4310/ajm.2020.v24.n2.a8
Yuri Prokhorov, C. Shramov
We prove that automorphism groups of Inoue and primary Kodaira surfaces are Jordan.
证明了Inoue曲面和初级Kodaira曲面的自同构群是Jordan的。
{"title":"Automorphism groups of Inoue and Kodaira surfaces","authors":"Yuri Prokhorov, C. Shramov","doi":"10.4310/ajm.2020.v24.n2.a8","DOIUrl":"https://doi.org/10.4310/ajm.2020.v24.n2.a8","url":null,"abstract":"We prove that automorphism groups of Inoue and primary Kodaira surfaces are Jordan.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2018-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43176230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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